The 26-year-old Twilight actress and the Australian TV personality were photographed holding hands while going out for lunch together at Vivian's Cafe in Studio City, Calif on Sunday, Sept. 29. Greene, wearing a light T-shirt, jeans and black boots, had a smile on her face while walking with Khoury, who dressed casually in a black tank top and grey sweatpants.

"They are dating," a source tells Us, but added that it isn't "that serious" just yet.

The couple's casual lunch outing, however, sparked engagement rumors. Despite the casual ensemble, Greene wore a large diamond ring on her left ring finger. A second source tells Us that they are dating, "but not engaged."

Though she's wearing a diamond ring, an insider tells Us Ashley Greens is not engaged to boyfriend Paul Khoury. Credit: Splash News

Khoury was famously photographed in a car with Cyrus, 20, leaving a house party in North Hollywood on March 7. At the time, the "We Can't Stop" singer's relationship with Hemsworth, 23, was on the rocks and she wasn't wearing her engagement ring. Earlier this month, a source tells Us Khoury celebrated his birthday in Las Vegas with Greene and Hemsworth.

During a March 2011 interview with Teen Vogue, Greene said she bonded with costar Cyrus, who was just 18 at the time, while filming the 2012 comedy LOL. "She's young, but we could relate to each other because she's probably been through as much as a 40-year-old!" she explained.

Greene has been through a lot in her own relationships with hunks like Reeve Carney, Jared Followill and Joe Jonas. In the November 2012 issue of Manhattan magazine, she shared what she's looking for in a man. "You need someone who is going to help you make that better version of yourself," Greene said. "I need someone who is strong but supportive and who loves me -- someone who isn't afraid to call me on my s--t."